In a known rotary piston internal combustion engine of the type described in U.S. Pat. No. 3,791,145, in order to improve afterburning of unburned exhaust constituents, after cold starting and while running warm from the region under compression of the inner chamber of the engine, fresh gas is introduced into the exhaust gas reactor by way of a line provided for the purpose. At the same time, under the action of the compression pressure or in response to the angular position of the eccentric shaft of the engine, a valve arranged in the line is periodically opened. An additional shut-off means arranged in this line and responding to the operating temperature of the exhaust gas reactor is provided, shutting off the supply of fresh gas when the warm-up phase is ended and the exhaust gas reactor has reached a certain temperature. However, the diversion of fresh gas from the inner chamber entails a diminution of the quantity of available ignitable fresh gas inside the working chamber, and this means a sacrifice of power. Then if during the warm-up phase or shortly after a cold start, a high output demand is placed on the engine, the expected full power will not be available because the shut-off means influenced by the operating temperature of the exhaust gas reactor is still open, permitting withdrawal of frersh gas. The associated loss of charge and consequently power may have adverse effects especially when the engine is used for propulsion of a motor vehicle in road traffic.